GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 26 Jan 2020, 07:33

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

If x, y and z are positive numbers, is x/y > (x + z)/(y + z) ?

Author Message
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 60646
If x, y and z are positive numbers, is x/y > (x + z)/(y + z) ?  [#permalink]

Show Tags

26 Nov 2018, 01:25
00:00

Difficulty:

35% (medium)

Question Stats:

68% (01:23) correct 32% (01:46) wrong based on 151 sessions

HideShow timer Statistics

If x, y and z are positive numbers, is $$\frac{x}{y} > \frac{x + z}{y + z}$$ ?

(1) x > z

(2) x > y

_________________
Manager
Joined: 19 Nov 2017
Posts: 249
Location: India
Schools: ISB
GMAT 1: 670 Q49 V32
GPA: 4
Re: If x, y and z are positive numbers, is x/y > (x + z)/(y + z) ?  [#permalink]

Show Tags

26 Nov 2018, 01:39
1
Bunuel wrote:
If x, y and z are positive numbers, is $$\frac{x}{y} > \frac{x + z}{y + z}$$ ?

(1) x > z

(2) x > y

$$\frac{x}{y} > \frac{x + z}{y + z}$$
Cross multiplying
xy + xz > xy + yz
xy + xz > xy + yz
x>y

Hence, B
_________________

Vaibhav

Sky is the limit. 800 is the limit.

~GMAC
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 5733
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: If x, y and z are positive numbers, is x/y > (x + z)/(y + z) ?  [#permalink]

Show Tags

26 Nov 2018, 18:34
Bunuel wrote:
If x, y and z are positive numbers, is $$\frac{x}{y} > \frac{x + z}{y + z}$$ ?

(1) x > z

(2) x > y

From given eqn we can deduce the following:
xy+xz>xy+yz
z(x-y)>0--(A)

so using 1: x>z , we are not given any relation about y so in -sufficient

From 1: X>Y
for any value of X >Y value the equation ( A) would stand true so B is sufficient..
Math Expert
Joined: 02 Sep 2009
Posts: 60646
Re: If x, y and z are positive numbers, is x/y > (x + z)/(y + z) ?  [#permalink]

Show Tags

24 Dec 2018, 01:45
Bunuel wrote:
If x, y and z are positive numbers, is $$\frac{x}{y} > \frac{x + z}{y + z}$$ ?

(1) x > z

(2) x > y

_________________
Manager
Joined: 24 Dec 2018
Posts: 107
Concentration: Entrepreneurship, Finance
GMAT 1: 710 Q47 V40
If x, y and z are positive numbers, is x/y > (x + z)/(y + z) ?  [#permalink]

Show Tags

29 Dec 2018, 04:47
1
1
There are two methods to solve this question.

Method 1:

Since x, y, z are all positive numbers, we can easily carry their denominators over the inequality without the fear of messing with the inequality.

Hence, $$\frac{x}{y} > \frac{x + z}{y + z}$$ can be written as x(y+z)>y(x+z)
This implies xy+xz>xy+yz

Again, xy is a positive number here, so we cancel it out from both sides, leaving us with xz>yz. Taking the expression to one side of inequality, we get xz-yz>0

Thus, either z>0 and x>y or z<0 and x<y.

Now, we are given that z>0 (its a positive number). Hence, for the expression to be definitely true, we must also get x>y. And statement 2 does that for us.

Hence statement 2 is sufficient

Method 2:

Now, if we add the same positive number z to x and y in the fraction x/y, $$\frac{x + z}{y + z}$$ will come closer to 1.

This gives us two possibilities:

1) If x/y<1, then $$\frac{(x+z)}{(y+z)}$$ is greater than x/y

and

2) If x/y>1, then $$\frac{(x+z)}{(y+z)}$$ is smaller than x/y

In our case, 2) works and this is satisfied only by statement 2. Hence, sufficient

Note: For anyone looking for more explanation on concept I used in statement 2, there is an article I think written by Karishma somewhere on GMATclub explaining this. If interested, I can look it up.
Intern
Joined: 11 Feb 2019
Posts: 13
Location: United Arab Emirates
Re: If x, y and z are positive numbers, is x/y > (x + z)/(y + z) ?  [#permalink]

Show Tags

26 Feb 2019, 01:37
For x/y to be greater, x/y needs to be greater than 1 or x>y

S1 irrelevant
S2 x>y hence a definitive Yes -> sufficient
Re: If x, y and z are positive numbers, is x/y > (x + z)/(y + z) ?   [#permalink] 26 Feb 2019, 01:37
Display posts from previous: Sort by